The once squeaky-clean Spanish royal family has become immersed in a growing fraud scandal that reveals how members of King Juan Carlos’s family may have cashed in on the monarchy’s good name.

At the centre of the scandal is the king’s son-in-law Iñaki Urdangarin, a former Olympic-medal-winning handball player who became the Duke of Palma after marrying Juan Carlos’s sporty daughter, the infanta Cristina.

Urdangarin and his business partners are the subject of daily leaks from a fraud investigation involving millions of euros of public money as Spain’s royal family struggles to hold on to its popularity.

Police have raided the offices of his private companies and of a foundation he once presided over, taking away documents.

El País newspaper reported this week that prosecutors believe Urdangarin, who has not been charged with any wrongdoing, will be named as a formal suspect in the case within two months. That could be a first step towards formal charges being placed.

The royal palace, meanwhile, added fuel to the scandal this week by suggesting Juan Carlos planned to cut the official royal family down to a nuclear core – in effect casting off his son-in-law and daughter.

On Thursday morning the palace press office appeared to have received a royal ticking off and publicly backtracked, saying “it deeply regretted having contributed to the fact that some media outlets reported this erroneously”.

Urdangarin himself, who now works for Spain’s Telefonica phone company in Washington DC, has said he is innocent.

“When I know the details of the investigations being carried out … I will be able to comment on their contents,” he said last month. “My professional behaviour has always been correct.”

Queen Sofia, meanwhile, has showed public support for her beleaguered daughter and son-in-law, allowing the latest edition of Hola magazine to publish pictures of her visiting them at their home in the US.

Speculation in Spanish newspapers has included predictions that Urdangarin will drop his aristocratic title so he can continue as a businessman or that Cristina will renounce her position as seventh in the line to the throne.

Within a few years of abandoning his sports career in 2000, and after studying at a prestigious business school, Urdangarin became the owner of a €6m (£5m) house in Barcelona. He set up various companies and became president of a nonprofit foundation, the Nóos Institute.

The institute boasted that its patrons included Urdangarin, his wife, an accountant described as an “assessor to the royal household” and professors from two of the world’s top business schools, the Barcelona-based Iese and Esade schools.

Nóos landed multimillion-euro contracts to organise events for regional governments in the Balearic Islands and Valencia.

But public prosecutors in Palma, the capital of the Balearics, have said there is evidence the institute was a front, charging hugely inflated fees and siphoning money off to Urdangarin’s private companies.

A €1.2m contract with the Balearic Islands was, prosecutors told investigating magistrate José Castro, “totally disproportionate to the task … based exclusively on a fictitious budget which did not analyse a single cost”.

They said evidence pointed to the foundation being used exclusively to channel money to other companies – many in the names of Urdangarin or his business partners.

“That was the sole aim,” they said.

At least €3.2m out of €5m was passed on from Nóos to Urdangarin’s companies, according to Publico newspaper.

The scandal comes as the royal family loses support among ordinary Spaniards. A regular poll by the state-run Centre for Sociological Investigation shows that, for the first time since polling started 17 years ago, trust in the royals has fallen below the halfway mark. Spaniards now place greater trust in the press.